I know it's been a little while since you asked the question, but just to follow on from TheGamesBond. As they state, they simply don't want to replace the entire lot of banknotes in the UK on a whim (Approx. 4.6 billion individual physical notes*), especially given that it would be fairly environmentally unfriendly. Given Charles' known love of the environment, it's not surprising he asked for them not to replace the ER II notes for “no reason”. I mean, we all know he's King whether it's his face on the money or not.
Also the first, and so far only, coin featuring CR III coin to go into general circulation was a commemorative issue. They didn't go particularly overboard with it either. The quantity is somewhat comparable to many of the recent commemorative releases (e.g. Each of the four featuring Paddington).
If you think about it in that way, it's perhaps not as weird. The Royal Mint has released one commemorative coin featuring CR III for general circulation. The Royal Mint has issued exactly zero new “standard” coins for general circulation at the time of writing. However, the BoE does not issue commemorative notes, only standard circulation notes. From that perspective, neither standard coins or banknotes featuring CR III have actually been released.
The new standard coins will probably begin to roll out over the next few years, as will the new standard banknotes. I believe I'm correct in saying the new standard £1 coins are expected to come out in late 2023 (though I've not heard about any of the other coins) and the first new standard banknotes will come out summer 2024. As such, there's not actually as big a gap as you might first think.
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*Billion using the short-scale method. I.e. 4,600,000,000 or 4.6 thousand-million, NOT million-million. According to the BoE themselves.